There is no such (simple) component in the JDK - if you don't need color, a JTextArea can be used to display ASCII-Art (after setting a fixed-width font). You will need to take care not to run into characterset issues (if you don't stick to US-ASCII 7-bit).
Writing a component that handles color display (and maybe escape sequences, in essence emulates a console window) wouldn't be too hard, but if you just started with Java it may prove to be an unwelcome challenge.
You could also just write your game in Java and leave displaying the ASCII to the system console (your game would simple output to stdout).
Edit: Color ASCII could be acieved by converting your internal format to (simple) HTML and that HTML could be displayed using a JLabel. Its probably not the most elegant method, but it should be reasonably simple to implement (and with nowadays hardware speed should not be an issue with this approach either). This approach builds on the capability that you can just use JLabel.setText() and pass a string that starts with a HTML tag. The JLabel then interprets the whole text as HTML.